02: Let f(x)= x' – 7x+ 2, 0sxs1. 1. Show that f(x) has exactly one real root in the indicated interval.

Q: The absolute minimum value of the function f(x) = –3 sinx on the interval [2, 8] is

A: To find the absolute minimum value of f(x), first we have to find the derivative of f(x) i.e. f'(x).…

Q: 2) Compute the approximate derivatives of In x I+ x2 fCx) at x-2, using three- endpoint formula…

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Q: Determine the absolute extreme values of the function f(x) = sinx - cosx + 6 on the interval 0 ≤ x ≤…

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Q: 2. Find the MacLaurin polynomial of degree 7 for the function F(x) So sin (6t²) dt.

A: SOLUTION-

Q: Show that f(x) = sin x (1 + cos x) is maximum when x = Hence find its maximum value.

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Q: Find the Absolute Extremum of F(x)=2sinx-cos2x over [0,2pi]

A: Consider the following:  Differentiate the function and find critical point:…

Q: 26. Show that the function has removable discontinuity at the origin sin 2x 2x f(x) = {Z 1 if x = 0…

A: Given f(0)=1 now we have find   limx→0f(x)=limx→0(sin2x2x)=1  ( By property)

Q: Vx + 2 Determine where f(x) = is continuous. In(3x – 5)

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Q: f(x)% 3D tanh In(2x) is equivalent to

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Q: Find the fourth derivative of f (z) = 37 + In(z) – 164z. Enclose arguments of functions in…

A: To Determine: find the fourth derivative of the function .  Given: we have a function…

Q: 2. Calculate the first derivative of f using the forward and backward difference approach in the…

A: The objective is to calculate the first derivative of f using the forward and backward difference…

Q: The function f(x)=(x)/(x-1) is discontinous at x=1 because

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Q: use graphical approximation methods to find the point(s) of intersction of f(x)=e^x and g(x)=x^6 to…

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Q: Find the global maximum and minimum of the function on the given…

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Q: If y = √√1-x² sin¹¹x, prove that (1-x²)+xy=1-x². dx

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Q: 5. Prove f(x) = e* + x has a root on the interval (-1,0) using the Intermediate Value Theorem.

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Q: Consider the function f(x) = cos x - 3x + 1. Since f (0)f() <0, f(x) has a root in [0]. If we use…

A: The function f(x)is given. Also given f(0)f(π2)&lt;0 Here f(0)=2 First we take x0=0+π22 Then we find…

Q: 1. Show that a frination fiłamb ]->1R is differentiable at xolamb) is and only if its lower and…

A: Solution: f:[a,b]→ℝ is differentiable at x0(a,b). Let us take upper derivative at x0+. Then,…

Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (²-) < 0, ƒ (x) has a root in [0]. If we…

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Q: State why the function 2z2 - 3z + e-z is analytic everywhere.

A: See the answer below

Q: 4. Determine all the critical numbe f(x)=x-sin(2x) on [0,27].

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Q: Prove that sinh−1(x) = In( x+Vx2 +1)

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Q: Consider the function f(x) = cos x - 3x + 1. Since f (0)ƒ < 0, f(x) has a root in [0]. If we use…

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Q: 25.) Use R3 to find a bound on error when P3 = x – x³ is used to approx f(x) = sin x on the interval…

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Q: Show that f(x) = x – cos(x) has only 1 real zero on the interval [0, .

A: given fx=x-cosxx∈0,π2

Q: FInd the length of the curve y= 2ln ( sin(x/2)) from x = π/5 to x = π

A: Formula to find the length of the curve is  ∫ab1+dydx2dxGiven y=2ln(sinx2) Lets find out dy/dx by…

Q: At which point does f(x)=2sinx-cos the maximum value over the interval [0.2 * pi]? 2x have an…

A: f(x)=2sin(x)-cos2(x) f'(x)=2cos(x)+2sin2(x) Now to find the critical number, f'(x)=0

Q: :Show that the function 1 x sin When x + 0 S(x) =- 0, is continuous but not differentiable at x = 0.…

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Q: Find the interval in which function f(x)=sin (log,x)+cos(log,x) is decreasing

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Q: The finite difference approximation of the first derivative in the simple implicit method used to…

A: given  ∂2u∂x2=∂u∂t to find the finite difference approximation of the first derivative in the…

Q: Find the value of K that make the function f continuous at x=2 -4 スー3x+2 sin(nx) + kx + k if x 2

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Q: Show that the function f(x) = exp(-|x|) is not differentiable at x = 0.

A: Given function is  fx=e-x given point is x=0.

Q: find the limit as x approaches 0. 12sin(3x)/1-cos(3x) = as x approaches 0

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Q: 12. Let f (x) = x + find all the critical %3D points and use the second derivative test to prove if…

A: We have to find critical points and state whether they are maximum or minimum using second…

Q: 2) Find the domain of the real-valued function defined as f (x) = arc cos 2x/(1+x^2 )+ log…

A: First find the domain of f1x=cos-12x1+x2: The domain of cos-1x is -1,1. Therefore, -1≤2x1+x2≤1 Now,…

Q: Find the local linear approximation of f(x) = tan¯(x – 4) at xo = 5, where Ax = x – 5. Enter the…

A: Given: fx=tan-1x-4

Q: Find the linearization of ƒ(x) = sqrt(1 + x) + sin x - 0.5 at x = 0

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Q: Find the absolute maximum of the function. fAx) = sin(6x) + cos(6x) on the interval 0. 18 %3D

A: Given: f(x)=sin(6x)+cos(6x) Differentiae the function.…

Q: Find points of discontunity of the function,where k is real number 1 f(x, y) sin(4 – x2 – y?) - -

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Q: 4. By the definition of derivative prove that f(x) = √x² +5 is differen- tiable at x=2.

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Q: Let [x² + 1 _ if x 1 f(x) - Is f differentiable at 1?:

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Q: Compute the second derivative with respect to r of 3x + 8 y = at x = 1.

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Q: Find the length of the curve defined as: f (x) = 5x from x = 0 to x = 1

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Q: 3. Verify the statement by showing that the derivative of the right side is equal to the integrand…

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Q: Consider the function f(x) = cos x - 3x + 1. Since f (0)ƒ < 0, f(x) has a root in [0]. If we use…

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Q: Consider the function f(x) = cos x − 3x + 1. Since f (0)ƒ () <0, f(x) has a root in [0]. If we use…

A: Here f(x) is a continuous function . If f(a)f(b)&lt;0 then f(x) has a root in [a,b]. Now we use…

Q: defines 2 as y. y- cos (3x2) = 5 a function of x and • differentiate implicity to find az ду

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Q: Find Tn cebtered at x=0 fir akk b for the function f(x) = 1/(1+x) at a=0

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